The following is offered as an example of the push to raise mathematical standards and improve American math performance.
From http://www.math.umt.edu/tmme/vol1no1/tmmev1n1a1.pdf, “Teaching Symmetry In the Elementary Curriculum,” by Christy Knuchel: According to the National Council of Teachers of Mathematics grades 3-5 should be able to apply transformations and use symmetry to analyze mathematical situations. This includes predicting and describing the results of sliding, flipping, and turning two-dimensional shapes. They should also be able to describe a motion or a series of motions that will show that two shapes are congruent, and identify and describe line and rotational symmetry in 2 and 3-dimensional shapes and designs. The Montana State Standards for Mathematics are in line with NCTM’s standards indicating that by the end of grade 4 students will be able to identify lines of symmetry, congruent and similar shapes, and positional relationships.